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Chapter 18 Measuring and Managing Operating Exposure to the

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					Chapter 18 Measuring and Managing Operating Exposure to the
           Exchange Rate

Quiz Questions
True-False Questions

_______        1.    A firm that has no operations abroad does not face any operating exposure.

_______        2.    Only firms with exports, or firms that compete against foreign exporters,
                     face operating exposure.

_______        3.    A firm that denominates all of its contracts in home currency, or hedges all of
                     its foreign currency contracts, faces no operating exposure.

_______        4.    Almost every firm faces some operating exposure, although some firms are
                     exposed only indirectly (through the country's general economic activity).

_______        5.    As large economies have a big impact on world economic activity, companies
                     in such a country tend to be very exposed to exchange rates.

_______        6.    Small economies tend to fix their exchange rate relative to the currency of
                     larger economies, or tend to create currency zones (like the EMS). Therefore,
                     companies in small economies tend to be less exposed to exchange rates.

_______        7.    The smaller a country, the more open the economy. Therefore, exposure is
                     relevant for firms.

_______        8.    Everything else being the same, the larger the monopolistic power of a firm,
                     the smaller its exposure because such a firm has more degrees of freedom in
                     adjusting its marketing policy.

_______        9.    Consider an exporting firm that has substantial monopolistic power in its
                     product market. Everything else being the same, the more elastic foreign
                     demand is, the more an exporting firm will profit from a devaluation of its
                     own currency. Similarly, the less elastic foreign demand is, the less an
                     exporting firm will be hurt by an appreciation of its own currency.

_______        10. Most information needed to measure operating exposure can be inferred from
                   the firm’s past export and import contracts.

A.       1. false; 2. false; 3. false; 4. true; 5. false; 6. false: the risk may be lower, but not the
         exposure; 7. true; 8. true; 9. false: not enough information1; 10. false.


Multiple Choice Questions
Choose the correct answer(s).

Q1.      In a small, completely open economy,


1 Let profits equal π = S × p*(x) - c(x) where x = exports. Profit maximization means S ∂x p (x) - ∂c(x) = 0.
                                                                                            *
                                                                                        ∂x       ∂x
                 ∂π                 ∂x p*(x) c(x) ∂x
      Therefore,    = x p*(x) + [ S         -    ]   = x p*(x). Without knowing what is held constant, it is
                 ∂S                    ∂x     ∂x ∂S
18-2                Exercises + Solutions                 International Financial Markets and the Firm


       (a) PPP holds relative to the surrounding countries.
       (b) A 10 percent devaluation of the host currency will be offset by a 10 percent rise in
           the host country prices.
       (c) The value of a foreign subsidiary, in units of the foreign parent’s home currency,
           is unaffected by exchange rate changes.
       (d) The real value of a foreign subsidiary to an investor from the host country is
           unaffected by exchange rate changes.
       (e) In the absence of contracts with a value fixed in host currency, the real value of a
           foreign subsidiary to an investor from the parent’s home country is unaffected by
           exchange rate changes.
       (f) In the absence of contracts with a value that is fixed in foreign currency, the real
           value of a foreign subsidiary to an investor from the host country is unaffected by
           exchange rate changes.
       (g) There is little or no advantage to using one's own currency: exchange rate policy
           has virtually no effects.

A1.    (a) and (g) are correct. (b) is wrong: the price rise will be 11.11 percent; (c) and (d)
       overlook contracts fixed in nominal terms; (e) and (f) should read "in the absence of
       contracts fixed in any currency".

Q2.    In a completely closed economy,
       (a) PPP holds relative to the surrounding countries.
       (b) A 10 percent devaluation of the host currency will be offset by a 10 percent rise in
             the host country prices.
       (c) The value of a foreign subsidiary, in units of the foreign parent’s home currency,
             is unaffected by exchange rate changes.
       (d) The real value of a foreign subsidiary to an investor from the host country is
             unaffected by exchange rate changes.
       (e) In the absence of contracts with a value fixed in host currency, the real value of a
             foreign subsidiary to an investor from the parent’s home country is unaffected by
             exchange rate changes.
       (f) In the absence of contracts with a value that is fixed in foreign currency, the real
             value of a foreign subsidiary to an investor from the host country is unaffected by
             exchange rate changes.
       (g) There is little or no advantage to having an own currency: exchange rate policy has
             virtually no effects.

A2.    (f), (g).

Q3.    In an economy that is neither perfectly open nor completely closed:
       (a) Consider a company that produces and sells in this economy. Apart from
            contractual exposure effects, its value in terms of its own (local) currency is
            positively exposed to the value of other currencies.
       (b) The value of an importing firm located in this economy could either go up or go
            down when the local currency devalues: the effect depends on such factors as the
            elasticity of local demand and foreign supply.
       (c) Consider a company that produces and sells in this economy. Apart from
            contractual exposure effects, its value in terms of a foreign currency is positively
            exposed to the value of its currency expressed in terms of other currencies.

A3.    (a), (b): when costs increase, the value of the firm cannot; (c): the home currency value
       could go up, but this effect may be smaller than the effect of a host country devaluation.

Q4.    Suppose that the value of the firm, expressed in terms of the owner’s currency, is a
       linear function of the exchange rate up to random noise:
       (a) The firm’s exposure is the constant at,T in VT(i) = at,T + bt,T ST(i) + et,T(i)
       (b) The exposure is hedged by buying forward bt,T units of foreign currency.
International Financial Markets and the Firm            Exercises + Solutions               18-3



A4.     (a), (b), and (c) are all false.

Q5.     Suppose that the value of the firm, expressed in terms of the owner’s currency, is a
        non-linear function of the exchange rate up to random noise. Suppose you fit a linear
        regression through this relationship, and you hedge with a forward sale with size equal
        to the regression coefficient.
        (a) All risk will be eliminated.
        (b) There is remaining risk, but it is entirely independent of the realized value of the
              exchange rate.
        (c) There is remaining risk, but it is uncorrelated the realized value of the exchange
              rate.
        (d) There is no way to further reduce the variance of the firm’s hedged value.
        (e) There is no way to further reduce the variance of the firm’s hedged value if only
              exchange rate hedges can be used.
        (f) There is no way to further reduce the variance of the firm’s hedged value if only
              linear exchange rate hedges can be used.

A5.     (c), (f).


Exercises

SynClear, of Seattle, Washington, produces equipment to clean up polluted waters. It has a
subsidiary in Canada that imports and markets its parent’s products. The value of this
subsidiary, in terms of CAD, has recently decreased to CAD 5m due to a depreciation in the
CAD relative to the USD (from the traditional level of USD/CAD 0.85 to about 0.75).
SynClear’s analysts argue that the value in CAD may very well return to its former level if, as
seems reasonable, the uncertainty created by Canada’s rising government deficit and Quebec’s
possible secession is resolved. If the CAD recovers, SynClear’s products would be less
expensive in terms of CAD, and the CAD value of the subsidiary would rise to about 6.5m.

E1.     From the parent’s (USD) perspective, is the exposure of SynClear Canada to the
        USD/CAD exchange rate positive or negative? What is the sign of the exposure?

A1.     Slow = 0.75; the value in USD is 5m × 0.75 =    USD 3.75.
        Shigh = 0.85; the value in USD is 6.5m × 0.85 = USD 5.525.

        Thus, the exposure is strongly positive. This is because SynClear Canada is an
        importing firm. The stronger the CAD, the more competitive US products are in
        Canada and, therefore, the more profits SynClear Canada will make.

E2.     Determine the exposure, and verify that the corresponding forward hedge eliminates
        this exposure. Use a forward rate of USD/CAD 0.80, and USD/CAD 0.75 and 0.85 as
        the possible future spot rates.

             5.525m – 3.75m
A2.     B=                    = CAD 17.75m.
               0.85 – 0.75
        If S = 0.75, the value in USD is 3.75 + 17.75 × (0.80 – 0.75) = USD 4.6375.
        If S = 0.75, the value in USD is 5.525 + 17.75 × (0.80 – 0.85) = USD 4.6375.

E3.     SynClear’s chairman argues that, as the exposure is positive and the only possible
        exchange rate change is an appreciation of the CAD, the only possible change is an
        increase in the value of the subsidiary. Therefore, he continues, the firm should not
        hedge: why give away the chance of gain? How do you evaluate this argument?
18-4                Exercises + Solutions                International Financial Markets and the Firm


A3.    The chairman overlooks two facts. First, only part of the gain from an appreciation is
       eliminated by the hedge. Second, if the appreciation does not materialize, SynClear will
       have a gain from the forward contract that alleviates the competitiveness problems
       associated with a low value of the CAD. In short, the hedge swaps part of the gain
       from an appreciation for a partial gain in case there is no appreciation.
            In the remainder of this series of exercises, SynClear Canada’s cash flows and
       market values are assumed, more realistically, to depend on other factors than just the
       exchange rate. The Canadian economy can be in a recession, or booming, or
       somewhere in between, and the state of the economy is a second determinant of the
       demand for SynClear’s products. The table below summarizes the value of the firm in
       each state and the probability of each state:

                                                                                     Conditional
        State of the economy                Boom      Medium         Recession       Expectation

        ST = 0.85: probability              0.075       0.175           0.25               n.a.
                   value (USD)              5.25        4.75            4.50

        ST = 0.75: probability              0.25        0.175           0.075              n.a.
                   value (USD)              4.25        3.857           3.50

E4.    What are the expected cash flows conditional on each value of the exchange rate?

A4.    USD 4.70m when ST = 0.85, and USD 4.00m when ST = 0.75.

E5.    Compute the exposure, the optimal forward hedge, and the value of the hedged firm in
       each state. The forward rate is still USD/CAD 0.80.

A5.    The exposure is:

                                      4.70 – 4.00
                                      0.85 – 0.75 = CAD 7m.

       (Vhedged | ST = 0.85)     = (Vunhedged | S=0.85) + 7m × (0.80 – 0.85)
                                 = 4.7 – 0.35.
       (Vhedged | ST = 0.75)     = (Vunhedged | S=0.75) + 7m × (0.80 – 0.75)
                                 = 4.0 + 0.35.

                                                                                     Conditional
        State of the economy                Boom      Medium         Recession       Expectation

        ST = 0.85: probability              0.075       0.175           0.25              n.a.
                   value (USD)              4.90        4.40            4.15              4.35

        ST = 0.75: probability              0.25        0.175           0.075             n.a.
                   value (USD)              4.60        4.207           3.85              4.35

       The conditional expectations have become independent of the exchange rate, but there
       still is as much sensitivity to the state of the economy as before, in the sense that the
       deviation of each possible outcome from its conditional expected value is the same as in
       the absence of hedging.


Mind-Expanding Exercises
International Financial Markets and the Firm                  Exercises + Solutions                 18-5


We modify the SynClear Canada example: there are five possible exchange rates, and SynClear
Canada’s value, in USD is a nonlinear function of the exchange rate. For simplicity, we ignore
risk caused by other factors than the exchange rate: from the text, or from Exercises 4 and 5,
we already know how to handle other risks. The value V as a function of the exchange rate S is
as follows:

          ST                        0.750        0.775        0.80         0.825           0.850
          Probability               0.10         0.20         0.40         0.20            0.10
          VT(ST ) (in USD)          4.00         4.25         4.45         4.60            4.70

ME1. Suppose SynClear USA wants to use a linear hedge. What is the linear regression of
     VT(ST ) on ST ? (Note that you have to take into account the fact that the outcomes are
     not equally probable. A correct but computationally simple way to do this is to compute
     a linear regression on your pocket calculator, as if you had ten equally probably
     outcomes where the case "ST = 0.775" occurs two times, the case "ST = 0.80" four
     times, and the case "ST = 0.825" two times.)

A1.     The linear regression is VT(ST ) = –1.18 + (7 × ST ) + residual.

ME2. (a) If the forward rate is USD/CAD 0.80, what is the value of the firm after this linear
         hedge?
     (b) What is the expected value?
     (c) Is the deviation from the mean predictable on the basis of the exchange rate?

A2.     (a) Add a forward sale with of CAD 7m.

          ST                        0.750        0.775        0.80         0.825        0.850
          VT(ST ) (in USD)          4.00         4.25         4.45         4.60         4.70
          –7m × (ST – 0.8)          0.35         0.175        0.00        –0.175       –0.35
          VT,hedged                 4.35         4.425        4.45         4.425        4.35

        (b) The expected value, hedged, is USD 4.42m.
        (c) Because we know what the deviation from the mean will be for each value of ST,
            the residuals are uncorrelated with ST, but not independent of ST.

ME3. (a) What portfolio of options would eliminate all uncertainty?
     (b) What is the future value of the hedged subsidiary?
     (c) The hedge that you engineered in part (b) locks in a rather low value for the
         subsidiary. Does this mean that hedging using a portfolio of options lowers the
         value of the participation?

A3.     (a) The single linear hedge considered in ME1 and ME2 fails to eliminate all risk
            because the exposure is not the same everywhere. For example, between the
            exchange rates 0.75 and 0.775, the exposure is:

                                      4.25 – 4.00
                                      0.775 – 0.75 = CAD 10m.

              Make similar computations for all other pairs of "adjacent" outcomes:

ST                                 0.750         0.775        0.80          0.825           0.850
VT (ST ) (in USD)                  4.00          4.25         4.45          4.60            4.70
Local exposure (CAD)                       10m           8m          6m               4m

              The local exposure of the hedge portfolio must be the negative of the local
              exposure of VT(S)T. Obtaining an exchange rate exposure equal to of CAD –10m
              by selling a call on CAD 10m with strike price X1 = 0.75 is too large, in absolute
18-6                 Exercises + Solutions                 International Financial Markets and the Firm


            value, for exchange rates that exceed 0.775. For ST > 0.775 we can lower the
            exposure to CAD –8m by adding a (long) call on CAD 2m with strike price X2 =
            0.775, and so on. The table below summarizes the solution:

                                    Local exposure of each call
           ST
              Size      Strike price     0.750     0.775     0.80      0.825     0.850
             -10m       X1=0.75               –10m      -10m      -10m      -10m
               2m       X2=0.775                0         2m        2m        2m
               2m       X 3=0.8                 0         0         2m        2m
               2m       X2=0.825                0         0         0         2m

           Total exposure of hedge            -10m          -8m           -6m            -4m

       (b) The future value of the hedged subsidiary now always equals USD 4.00.
       (c) No. The parent also obtains up-front revenue for writing the (relatively expensive)
           call on CAD 10m at X = 0.75. The cost of buying the additional calls does not
           offset this up-front revenue because (1) the higher the strike price, the lower the
           value of a call option, and (2) the three additional calls are for smaller amounts of
           CAD than CAD 10m. Thus, the total portfolio of calls surely generates up-front
           income, which compensates for the lower future value of the hedged firm.

ME4. To value the subsidiary, you could construct a replicating portfolio. How would you
     construct this portfolio?

A4.    First reverse all the signs of the option positions: buy a call on CAD 10m at X1 = 0.75,
       sell a call on CAD 2m at X2 = 0.775, and so on. The payoff from this option portfolio
       will have the same curvature as the value of the subsidiary, but the option portfolio has
       a zero value for ST = 0.75, whereas the subsidiary has a value of USD 4m for ST =
       0.75. That is, the payoff from the options portfolio is too low by USD 4m everywhere.
       To increase the payoff from the options portfolio by USD 4m everywhere, buy a USD
       bond with future value equal to 4m. The portfolio of the bond and the four options will
       perfectly replicate the value of the subsidiary.

				
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